Delta Method Standard Error Matlab
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non-linear transformation * Stata do file * The Delta method can be used to estimate the standard errors after a regression estimation. * Imagine you have some parameter delta method standard error of variance G = (3*b0-b1)*b2^2 = 3*b0*b2^2-b1*b2^2 * Where y = bo +
Delta Method Standard Error Stata
b1*x1 + b2*x2 + u * The delta method can be used to estimate the standard errors standard error matlab regression of G. * The delta method states that var_hat(G)=(dG/db) var(b) (dG/db) * dG/db is a gradient vector: * dG/db = [dG/db0, dG/db1, dG/db2] * dG/db = [b2^2, -b2^2,
Calculate Standard Error Matlab
2*(b0-b1)*b2] * var_hat(G) = (3*b2^2)^2 * se(b0)^-2 + (-b2^2)^2 * se(b1)^-2 + (2*(b0-b1)*b2)^2 * se(b2)^-2 [There is an error in the code because I failed to include a covariance term for the coefficients. Please see the more recent update on the method.] clear set obs 1000 gen x1 = rnormal() gen x2 = rnormal() * 4 global bootstrap standard error matlab b0 = 1 global b1 = 1.5 global b2 = .3 local true_G = (3*${b0}-${b1})*${b2}^2 di `true_G' gen y = ${b0} + ${b1}*x1 + ${b2}*x2 + rnormal()*8 reg y x1 x2 * G = (3*b0-b1)*b2^2 = 3*b0*b2^2 - b1*b2^2 local Ghat = (3*_b[_cons]-_b[x1])*_b[x2]^2 di "Ghat = `Ghat' is our estimate (true = `true_G')" * Let's see if we can't use the delta method to derive a standard error. local var_hatG = (3*_b[x2]^2)^2 * _se[_cons]^2 + (-_b[x2]^2)^2 * _se[x1]^2 + (2*(_b[_cons]-_b[x1])*_b[x2])^2 * _se[x2]^2 di "Standard error estimate is " `var_hatG'^.5 * Alternatively, let us attempt to bootstrap our standard errors. cap program drop deltaOLS program define deltaOLS, rclass reg y x1 x2 return scalar Ghat = (3*_b[_cons]-_b[x1])*_b[x2]^2 end bs Ghat=r(Ghat), rep(500): deltaOLS * The bootstrap standard errors are similar to that of the delta method's standard errors. cap program drop deltaMonteCarlo program define deltaMonteCarlo, rclass clear set obs 1000 gen x1 = rnormal() gen x2 = rnormal() * 4 gen y = ${b0
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Standard Deviation Matlab
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Confidence Interval Matlab
Machine Learning Toolbox Examples Functions and Other Reference Release Notes PDF Documentation Regression Nonlinear t test matlab Regression Nonlinear Models Statistics and Machine Learning Toolbox Functions nlpredci On this page Syntax Description Examples Confidence Interval for Nonlinear Regression Curve Prediction Interval http://www.econometricsbysimulation.com/2012/12/the-delta-method-to-estimate-standard.html for New Observation Simultaneous Confidence Intervals for Robust Fit Curve Confidence Interval Using Observation Weights Confidence Interval Using Nonconstant Error Model Input Arguments modelfun X beta R CovB J Name-Value Pair Arguments 'Alpha' 'ErrorModelInfo' 'MSE' 'PredOpt' 'SimOpt' 'Weights' Output Arguments Ypred delta More About Confidence Intervals for https://www.mathworks.com/help/stats/nlpredci.html Estimable Predictions Tips Algorithms References See Also This is machine translation Translated by Mouse over text to see original. Click the button below to return to the English verison of the page. Back to English × Translate This Page Select Language Bulgarian Catalan Chinese Simplified Chinese Traditional Czech Danish Dutch English Estonian Finnish French German Greek Haitian Creole Hindi Hmong Daw Hungarian Indonesian Italian Japanese Korean Latvian Lithuanian Malay Maltese Norwegian Polish Portuguese Romanian Russian Slovak Slovenian Spanish Swedish Thai Turkish Ukrainian Vietnamese Welsh MathWorks Machine Translation The automated translation of this page is provided by a general purpose third party translator tool. MathWorks does not warrant, and disclaims all liability for, the accuracy, suitability, or fitness for purpose of the translation. Translate nlpredciNonlinear regression prediction confidence intervalscollapse all in page Syntax[Ypred,delta] = nlpredci(modelfun,X,beta,R,'Covar',CovB) example[Ypred,delta] = nlpredci(modelfun,X,beta,R,'Covar',CovB,Name,Value) example[Ypred,delta] = nlpredci(modelfun,X,beta,R,'Jacobian',J) examp
estimator of a parameter by numerical methods. In this lecture we provide a fully worked out example that illustrates how to do so with MATLAB. In what follows, I will assume that you have access to a MATLAB installation comprising both the https://www.statlect.com/fundamentals-of-statistics/maximum-likelihood-matlab-example Statistics and the Optimization toolboxes (an installation of Octave - a free software that is very similar to MATLAB - should provide the same functionality). Data We have a sample of 100 independent draws from a standard Student's t distribution with degrees of freedom. The parameter is unknown and we want to estimate it by maximum likelihood. The data (the 100 observations) are stored in the MATLAB file data.mat, which you need to download. Parametrization standard error Note that the parameter must be strictly positive, that is, it must belong to the interval . Therefore, the optimization problem we need to solve in order to estimate is a constrained optimization problem. As explained in the lecture Maximum likelihood - Algorithm, it is preferable to avoid constrained problems when possible. In this case, it is possible because can be easily reparametrized aswhere is our new parameter and there are no constraints on it, because standard error matlab it can take any value in the interval . Coding the log-likelihood function The likelihood function is coded as a routine that takes as inputs a value for the parameter and the data, and returns as output the value of the log-likelihood with its sign changed. The code is as follows. function val=log_lik(theta,data) n=exp(theta); val=-sum(log(tpdf(data,n))); The name of the function is log_lik. It takes as arguments the parameter theta and the vector of observations data. The function tpdf (which is part of the Statistics toolbox) computes the probability density function of a Standard Student's t distribution. In particular, tpdf(data,n) returns a vector of densities (one density for each observation in the vector data), under the hypothesis that the number of degrees of freedom is equal to n. By taking the natural logarithm with the log function and summing over all entries of the vector, we obtain the log-likelihood of the sample. In other words, with the command sum(log(tpdf(data,df))) we compute the log-likelihoodwhere is an observation (a component of the vector data), is the sample size (the dimension of the vector data) and is the probability density function of , given that the parameter is equal to . Finally, we change the sign of the log-likelihood, by putting a minus in front of it, because the optimization routine we are going to use performs minimization by default